It is known to provide collapsible structures, for use in cots and beds, comprising first and second elongate members which each have first and second ends and are pivotally interconnected to form an X-frame. It is possible to transform such a structure from an extended condition, in which the first and second ends of the elongate members are disposed at the corners of an imaginary rectangle, to a collapsed condition in which the two first ends of the elongate members, and hence the two second ends, lie adjacent each other. However, although the X-frame becomes quite compact when the structure is in its collapsed condition, difficulty is encountered in arranging the other components of the structure, which are connected to the X-frame, so that the structure is compact when in its collapsed condition.